\section{Introduction}
This report is written for the course Computational Finance, a master course
at the University of Amsterdam. During the lectures we have learned three
methods to price options. These methods are `The binomial tree method', `Monte
Carlo option pricing' and `Finite-difference methods for option pricing'.\\
\noindent
In this report we explain the method of Finite Difference in great detail,
this report is the sequel to the previous report which explained the methods
of the `The binomial tree method' and the `Monte
Carlo option pricing'.\\
\noindent
In order to explain Finite Difference we first show how to get from the
Black-Scholes formulae to the Black-Scholes Partial Differential Equation, we
use this PDE to get to the different schemes of Finite Difference. The schemes
which we show in more detail are the Forward Time Centered Scheme and the
Crank-Nicolson scheme, with these schemes we calculate the prices of various
European call and put options. When this is done we explain the Greeks, which
reflect the sensitivity of an option, in great detail and we show how these
Greeks can be used for hedging. We finish with the application of Finite
Difference in the American and the Digital option. 



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